I try to think of how anarchy could work: It just can't (unless other evils cease to exist) .
What if I told you those "evils" exist because the government enables them to exist? For example: is killing evil? Perhaps. If someone goes on a killing spree and the police have to gun him down, is killing still wrong? I don't know. However, the government declares that killing is evil by labeling it "murder". Thus, citizens cannot "murder", but the government can kill. That's not a necessary evil; it's simply enabling evil.
The only necessary evil in this world is we, the people. The government is nothing more than a proxy for us to pretend the evil we commit (for example, outlawing marijuana, thus making drug dealers evil) is acceptable.
And then we have to define evil:
e·vil
/ˈēvəl/
Adjective
Profoundly immoral and malevolent.
Noun
Profound immorality, wickedness, and depravity, esp. when regarded as a supernatural force.
Because that which is "moral" and that which is "malevolent" are completely up to the individual (specifically, up to cultures,) it is absurd to believe the government has any role in deciding what is evil and what isn't on a global scale. After all, if the government is a necessary evil (which nobody can really define as evilness is not a universal concept, but a local one), would the government not commit evil acts and enable others to commit evil acts? Thus, to rid the world of evil (again, a personal interpretation,) you rid the monopoly on security. Even if you don't believe that anarchism couldn't work, could you imagine a world where people have the right to decide from the comfort of their homes which governments they follow? As opposed to being forced into one government, a national government, in which you have no choice but to participate in or uproot yourself and find another government to live in (which is undoubtedly similar to the American government, or considerably worse e.g. state communism.)
But on the point of "necessary evil": if we cannot define what is evil and what isn't, and if that definition cannot always be consistent, it is better to adopt another term. I don't believe the government is necessary, or evil. I do, however, disagree with much that the government does, and many things governments love to do, such as wage war, are downright "evil". These "evils" occur because 1% of the world controls 99% of people. We should strive for a 1:1 ratio, where, on average, a single person will have as much power for a single person's life, their own. To say anarchism cannot work because you don't see how it could work is a good start; at least you're not outright saying it's impossible.